I could not change the apple id to the old phone. I want to insert my daughter apple id as she will use the phone but it was failed. It keeps asking my apple id and password. What should I do?

This is an anti-theft measure. Apple has no idea that her new phone was handed down from you. In order for your daughter to register her own Apple ID on the phone, you must first remove your Apple ID from that phone.

On the phone you are giving to your daughter, go to Settings. Tap on your name at the top of the Settings page. All the way at the bottom of the next page, tap on "Sign Out". Follow the instructions. When you have successfully signed out of your Apple ID, your daughter will be able to sign in with hers. Good luck.

I followed all of the above steps but when I got to sign out it was grayed out and would allow me to select. Each time I change her Apple ID it changes it on my phone so it’s like we are linked but we have separate ID’s both that work. How do I unlink them?

Sorry wouldn’t allow me to select.